CN103135501A - Acceleration and deceleration controlling method based on S-shaped curve and equipment using the same and numerically-controlled machine tool - Google Patents

Abstract

The invention discloses an acceleration and deceleration controlling method based on an S-shaped curve. An S-shaped curve is applied to speed planning of an i+1 section of a processing track, wherein the i+1 section of the processing track is arranged between a first transfer position and a second transfer position, and accelerations of the first transfer position and the second transfer position are controlled not to be zero. The invention further discloses a controlling device of acceleration and deceleration based on the S-shaped curve and the numerically-controlled machine tool. Due to the fact that the acceleration and deceleration method based on the S-shaped curve and the equipment using the acceleration and deceleration controlling method based on the S-shaped curve of a numerically-controlled system control the accelerations of the first transfer position and the second transfer position not to be zero, processing efficiency can be effectively improved, and impact to the machine tool during the processing process is reduced.

Description

Acceleration-deceleration Control Method and device and numerically-controlled machine based on S type curve

Technical field

The present invention relates to the Computerized Numerical Control technology field, specifically relate to a kind of Acceleration-deceleration Control Method and device based on S type curve, also relate to a kind of numerically-controlled machine that adopts this acceleration/deceleration control device.

Background technology

Along with the development of High-speed Machining Technology, the trend of numerically-controlled machine High-speed machining is increasingly outstanding.Because the workpiece profile of processing is varied, the job sequence of each part is comprised of a plurality of program segments.These program segments are comprised of straight line and circular arc mostly, and there is switching place in the place that straight line is connected with circular arc.Numerically-controlled machine must carry out acceleration and deceleration and process in order to realize the high precision of workpiece processing in the motion control between switching place program segment, to guarantee that lathe does not produce impact, step-out, overclocking or vibration when starting or stoping.

In prior art, several method below employing is usually processed in the acceleration and deceleration of switching place: the first is that the speed of switching place is set to zero; The second is to adopt the constant speed transition in switching place, first the speed of switching place is limited, and then adopts S type or T-shaped curve to carry out speed planning to the machining locus before and after switching place.

Yet there is certain drawback in above-mentioned acceleration and deceleration disposal route: for the first, accelerate frequently and deceleration can strengthen machine motor load, produce noise and vibration, reduce machining precision, less electrical machinery life may not reach the process velocity of appointment by static acceleration simultaneously; For the second, in the boost phase acceleration of starting from scratch, need to expend the regular hour, cause working (machining) efficiency lower.

Summary of the invention

The invention provides a kind of Acceleration-deceleration Control Method based on S type curve and device and numerically-controlled machine, can effectively solve the problem that in and process low in switching place working (machining) efficiency, lathe is impacted.

For solving the problems of the technologies described above, an aspect of of the present present invention is: a kind of Acceleration-deceleration Control Method based on S type curve is provided, S type curve is used for the i+1 section machining locus between the first switching place and the second switching place is carried out speed planning, and the acceleration of this Acceleration-deceleration Control Method control first switching place and the second switching place is non-vanishing.

Wherein, the non-vanishing step of acceleration of control the first switching place and the second switching place specifically comprises: the speed v of calculating the first switching place _sSpeed v with the second switching place _eValue range; Speed v according to the first switching place _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value; Speed v according to the first switching place _s, the second switching place speed v _e, i+1 section machining locus initial acceleration a _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the acceleration of the first switching place and the second switching place is non-vanishing.

Wherein, calculate the speed v of the first switching place _sSpeed v with the second switching place _eThe step of value range specifically comprise: obtain the i section machining locus that is connected with i+1 section machining locus by the first switching place and the first switching angle α of i+1 section machining locus ₁, and the second switching angle α that obtains the i+2 section machining locus that is connected with i+1 section machining locus by the second switching place and i+1 section machining locus ₂According to the first switching angle α ₁With the second switching angle α ₂Calculate respectively the speed v of the first switching place _sSpeed v with the second switching place _eValue range.

Wherein, according to the speed v of the first switching place _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe step of maximum possible value specifically comprise: according to formula (1) ${\left|\stackrel{\→}{{\mathrm{\Δa}}_i}\right|}^2={\left|\stackrel{\→}{a_i}\right|}^2+{\left|\stackrel{\→}{a_{i+1}}\right|}^2-2\left|\stackrel{\→}{a_i}\right|\left|\stackrel{\→}{a_{i+1}}\right|\cos \frac{\mathrm{\π}-{\mathrm{\α}}_1}{2}$ And formula (2) $\left|\stackrel{\→}{{\mathrm{\Δa}}_i}\right|=\left|\stackrel{\→}{a_{i+1}}\right|\cos \frac{{\mathrm{\α}}_1}{2}=\frac{\left|\stackrel{\→}{v_a}\right|\sin {\mathrm{\α}}_1}{2T}$ Obtain a _iPossible maximal value, a _iValue and the initial acceleration a of i+1 section machining locus _sEquate, wherein,

Be acceleration corresponding to last interpolation cycle T of i section machining locus,

Be the acceleration of the first switching place, the position that last interpolation cycle T machining of i section machining locus arrives is the terminal point of i section machining locus; According to formula (3) ${\left|\stackrel{\→}{{\mathrm{\Δa}}_{i+1}}\right|}^2={\left|\stackrel{\→}{a_{i+1}}\right|}^2+{\left|\stackrel{\→}{a_{i+2}}\right|}^2-2\left|\stackrel{\→}{a_{i+1}}\right|\left|\stackrel{\→}{a_{i+2}}\right|\cos \frac{\mathrm{\π}-{\mathrm{\α}}_2}{2}$ And formula (4) $\left|\stackrel{\→}{{\mathrm{\Δa}}_{i+1}}\right|=\left|\stackrel{\→}{a_{i+2}}\right|\cos \frac{{\mathrm{\α}}_2}{2}=\frac{\left|\stackrel{\→}{v_{a+1}}\right|\sin {\mathrm{\α}}_2}{2T}$ Obtain a _i+1Possible maximal value, a _i+1Value and the terminal point acceleration a of i+1 section machining locus _eEquate, wherein,

Be acceleration corresponding to last interpolation cycle T of i+1 section machining locus,

Be the acceleration of the first switching place, the position that last interpolation cycle T machining of i+1 section machining locus arrives is the terminal point of i+1 section machining locus.

Wherein, according to the speed v of the first switching place _s, the second switching place speed v _e, i+1 section machining locus initial acceleration a _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the non-vanishing step of acceleration of the first switching place and the second switching place specifically comprises:

Initial acceleration a according to i+1 section machining locus _s, terminal point acceleration a _e, the first switching place speed v _sAnd the speed v of the second switching place _eWith i+1 section machining locus be divided into acceleration, even acceleration, subtract acceleration, at the uniform velocity, acceleration and deceleration, even deceleration and seven stages and obtain respectively following system of equations of slowing down:

The acceleration system of equations (5) of i+1 section machining locus:

$a\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}J{\mathrm{\&tau;}}_1+a_s,0\&le;t\&le;t_1\\ A,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ A-J{\mathrm{\&tau;}}_3,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\\ 0,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ -J{\mathrm{\&tau;}}_5,t_4\&le;t\&le;t_5\\ -D,t_5\&le;t\&le;t_6\\ -D+J{\mathrm{\&tau;}}_7,t_6\&le;t\&le;t_7\end{array}\right.$

The rate equation group (6) of i+1 section machining locus:

$f\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{f}_s+a_s{\mathrm{\&tau;}}_1+\frac{1}{2}J{\mathrm{\&tau;}}_1^2,0\&le;t\&le;t_1\\ {\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{\&tau;}}_2,{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=f_s+{\mathrm{<figure-callout\; id="1"\; label="a\; s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s{T}_{}{}_1+\frac{1}{2}\mathrm{<figure-callout\; id="1"\; label="J\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_1^2,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+A{\mathrm{\&tau;}}_3=\frac{1}{2}J{\mathrm{\&tau;}}_3^2,{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;t_3\\ {\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3,f={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+{\mathrm{AT}}_3-\frac{1}{2}\mathrm{<figure-callout\; id="3"\; label="J\; T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_3^2,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ f_4-\frac{1}{2}J{\mathrm{\&tau;}}_5^2,f=f_4,t_4\&le;t\&le;t_5\\ f_5-D{\mathrm{\&tau;}}_6,f_5=f_4-\frac{1}{2}J{T}_5^2,t_4\&le;t\&le;t_6\\ f_6-D{\mathrm{\&tau;}}_7+\frac{1}{2}J{\mathrm{\&tau;}}_7^2,f_6=f_5-D{T}_6,t_6\&le;t\&le;t_7\end{array}\right.$

The shifted systems (7) of i+1 section machining locus

$l\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{l}_s+v_s{\mathrm{\&tau;}}_1+\frac{1}{2}{a}_s{\mathrm{\&tau;}}_1^2+\frac{1}{6}J{\mathrm{\&tau;}}_1^3,0\&le;t\&le;t_1\\ {\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1{\mathrm{\&tau;}}_2+\frac{1}{2}A{\mathrm{\&tau;}}_1^2,{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=l_s+{\mathrm{<figure-callout\; id="1"\; label="v\; s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">v</figure-callout>}}_s{T}_{}{}_1+\frac{1}{2}{\mathrm{<figure-callout\; id="1"\; label="a\; s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s{T}_{}^{}{}_1^2+\frac{1}{6}\mathrm{<figure-callout\; id="1"\; label="J\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_1^3{,}^{}{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ {\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2{\mathrm{\&tau;}}_3+\frac{1}{2}A{\mathrm{\&tau;}}_3^2-\frac{1}{6}J{\mathrm{\&tau;}}_3^3,{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_2={\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+f_1{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2+\frac{1}{2}\mathrm{<figure-callout\; id="1"\; label="A\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">A</figure-callout>}{T}_{}^{}{}_1^2,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;t_3\\ {\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+{\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3{\mathrm{\&tau;}}_4,{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+f_2{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3+\frac{1}{2}A{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^2-\frac{1}{6}\mathrm{<figure-callout\; id="3"\; label="J\; T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_3^3,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ l_4+f_4{\mathrm{\&tau;}}_5-\frac{1}{6}J{\mathrm{\&tau;}}_5^3,f={\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+f_3{T}_4,t_4\&le;t\&le;t_5\\ l_5+f_5{\mathrm{\&tau;}}_6-\frac{1}{62}D{\mathrm{\&tau;}}_6^2,f_5=l_4+f_4{T}_5-\frac{1}{6}J{T}_5^3,t_5\&le;t\&le;t_6\\ l_6+f_6{\mathrm{\&tau;}}_7-\frac{1}{2}D{\mathrm{\&tau;}}_7^2+\frac{1}{6}J{\mathrm{\&tau;}}_7^2,f_6=l_5+f_5{T}_6-\frac{1}{2}D{T}_6^2,t_6\&le;t\&le;t_7\end{array}\right.$

Wherein, t is time coordinate, t _i(i=1,2,3 ..., 7) and be the time coordinate at each stage end, τ _iExpression local time is to deduct τ with time t in each stage _iThe time value that obtains, T _i(i=1,2,3 ..., 7) and represent the time span that each stage continues, A is peak acceleration, and D is maximum deceleration, and J is maximum acceleration;

According to acceleration system of equations (5), rate equation group (6) and shifted systems (7), i+1 section machining locus is carried out the planning of S type curve speed.

Wherein, according to acceleration system of equations (5), rate equation group (6) and shifted systems (7), the step that i+1 section machining locus carries out the planning of S type curve speed is specifically comprised:

Interval differentiation: the time span that each stage continues is calculated in interval differentiation, obtains according to acceleration system of equations (5):

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=\frac{A-a_s}{J},$ ${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3=\frac{A}{J},$ $T_5=\frac{D}{J},$ $T_7=\frac{D-a_e}{J},$

Wherein, T ₁The time span that continues for adding boost phase, T ₃The time span that continues for subtracting boost phase, T ₅Be lasting time span of acceleration and deceleration stage, T ₇For subtracting the time span that the decelerating phase continues;

Reach speed f at even boost phase end ₃, according to rate equation group (6) and shifted systems (7), obtain:

f ₃=f （8）；

${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\frac{f-v_s}{A}-\frac{A}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2\mathrm{AJ}}---\left(9\right);$

Wherein, f is speed of feed, T ₂For the lasting time span of even boost phase, if T ₂﹤ 0, passes through formula $A=\mathrm{sgn}\left(A\right)\sqrt{J-(f-v_s)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2}}---\left(10\right)$

The value of adjusting peak acceleration A is the maximum possible value, and substitution formula (9) recomputates T ₂Value;

Reach speed v subtracting decelerating phase end _e, according to rate equation group (6) and shifted systems (7), obtain:

$T_6=\frac{f-v_e}{D}-\frac{D}{J}+\frac{a_e^2}{2\mathrm{DJ}}---\left(11\right)$

Wherein, T ₆For lasting time span of even decelerating phase, if T ₆﹤ 0, passes through formula

$D=\mathrm{sgn}\left(D\right)\sqrt{J(f-v_e)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2}}---\left(12\right)$

The value of adjusting maximum deceleration D is the maximum possible value, and substitution formula (11) is counted T again ₆Value;

With T ₁, T ₂, T ₃, T ₅, T ₆, T ₇Value substitution rate equation group (6), in conjunction with $L=\underset{k=1}{\overset{7}{\mathrm{\&Sigma;}}}{l}_k-l_{k-1}=l_7-l_s,$ Can get:

$T_4=\frac{1}{f}(\frac{v_e{a}_e+v_s{a}_s}{J}-\frac{{\mathrm{<figure-callout\; id="3"\; label="a\; e"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_e^{}+{\mathrm{<figure-callout\; id="3"\; label="a\; s"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s^{}}{3J^2})-$

$\frac{1}{f}[\frac{1}{2A+2\mathrm{<figure-callout\; id="2"\; label="D\; f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">D</figure-callout>}}{f}^{}{}^2+(\frac{A}{2J}+\frac{D}{2J})f+\frac{A(v_s-\frac{{\mathrm{<figure-callout\; id="2"\; label="a\; s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s^{}}{2J})}{2J}+\frac{D(v_e-\frac{{\mathrm{<figure-callout\; id="2"\; label="a\; e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_e^{}}{2J})}{2J}-\frac{{(v_s-\frac{{\mathrm{<figure-callout\; id="2"\; label="a\; s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s^{}}{2J})}^2}{2A}-\frac{(v_e-\frac{{\mathrm{<figure-callout\; id="2"\; label="a\; e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_e^{}}{2J})}{2D}]$

Wherein, T ₄Be the length of duration in stage at the uniform velocity, L is the length of i+1 section machining locus, l ₇For subtracting displacement corresponding to decelerating phase, l _sBe initial position, if T ₄﹤ 0, and the value of adjusting speed of feed f makes T ₄=0, and recomputate T ₁, T ₂, T ₃, T ₅, T ₆And T ₇Value;

Real-time interpolation: according to T ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value S type curve carried out real-time interpolation calculate.

For solving the problems of the technologies described above, another aspect of the present invention is: a kind of acceleration/deceleration control device based on S type curve is provided, S type curve is used for the i+1 section machining locus between the first switching place and the second switching place is carried out speed planning, this acceleration/deceleration control device comprises: switching place speed calculation module is used for calculating the speed v of the first switching place _sSpeed v with the second switching place _eValue range; The acceleration calculation module is used for the speed v according to the first switching place of switching place speed calculation module calculating acquisition _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value; The speed planning module is used for the speed v according to the first switching place of switching place speed calculation module calculating acquisition _sSpeed v with the second switching place _eValue range and the initial acceleration a of the i+1 section machining locus that obtains of acceleration calculation module _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the acceleration of the first switching place and the second switching place is non-vanishing.

Wherein, speed calculation module comprises: switching angle acquiring unit is used for obtaining first of the i section machining locus that is connected with i+1 section machining locus by the first switching place and the i+1 section machining locus angle α that transfers ₁, and the second switching angle α that obtains the i+2 section machining locus that is connected with i+1 section machining locus by the second switching place and i+1 section machining locus ₂The speed computing unit is used for the first switching angle α that obtains according to the angle acquiring unit of transferring ₁With the second switching angle α ₂Calculate respectively the speed v of the first switching place _sSpeed v with the second switching place _eValue range.

Wherein, the acceleration calculation module comprises:

The initial acceleration computing unit, the initial acceleration computing unit is used for according to formula (1) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2={\left|\stackrel{\&RightArrow;}{a_i}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_i}\right|\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}$ And formula (2) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_1}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_a}\right|\sin {\mathrm{\&alpha;}}_1}{2T}$ Obtain a _iPossible maximal value, a _iValue and the initial acceleration a of i+1 section machining locus _sEquate, wherein,

Be acceleration corresponding to last interpolation cycle T of i section machining locus,

Be the acceleration of the first switching place, the position that last interpolation cycle T machining of i section machining locus arrives is the terminal point of i section machining locus;

Terminal point acceleration calculation unit, terminal point acceleration calculation unit is used for according to formula (3) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|}^2={\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_2}{2}$ And

Formula (4) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|=\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{{\mathrm{\&alpha;}}_2}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_{a+1}}\right|\sin {\mathrm{\&alpha;}}_2}{2T}$ Obtain a _i+1Possible maximal value, a _i+1Value and the terminal point acceleration a of i+1 section machining locus _eEquate, wherein,

Be acceleration corresponding to last interpolation cycle T of i+1 section machining locus, Be the acceleration of the first switching place, the position that last interpolation cycle T machining of i+1 section machining locus arrives is the terminal point of i+1 section machining locus.

Wherein, the speed planning module comprises:

Stage system of equations acquiring unit is used for the initial acceleration a according to i+1 section machining locus _s, terminal point acceleration a _e, the first switching place speed v _sAnd the speed v of the second switching place _eWith i+1 section machining locus be divided into acceleration, even acceleration, subtract acceleration, at the uniform velocity, acceleration and deceleration, even deceleration and seven stages and obtain respectively following system of equations of slowing down:

The acceleration system of equations (5) of i+1 section machining locus:

$a\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}J{\mathrm{\&tau;}}_1+a_s,0\&le;t\&le;t_1\\ A,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ A-J{\mathrm{\&tau;}}_3,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\\ 0,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ -J{\mathrm{\&tau;}}_5,t_4\&le;t\&le;t_5\\ -D,t_5\&le;t\&le;t_6\\ -D+J{\mathrm{\&tau;}}_7,t_6\&le;t\&le;t_7\end{array}\right.$

The rate equation group (6) of i+1 section machining locus:

$f\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{f}_s+a_s{\mathrm{\&tau;}}_1+\frac{1}{2}J{\mathrm{\&tau;}}_1^2,0\&le;t\&le;t_1\\ {\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{\&tau;}}_2,{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=f_s+{\mathrm{<figure-callout\; id="1"\; label="a\; s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s{T}_{}{}_1+\frac{1}{2}\mathrm{<figure-callout\; id="1"\; label="J\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_1^2,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+A{\mathrm{\&tau;}}_3=\frac{1}{2}J{\mathrm{\&tau;}}_3^2,{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;t_3\\ {\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3,f={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+{\mathrm{AT}}_3-\frac{1}{2}\mathrm{<figure-callout\; id="3"\; label="J\; T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_3^2,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ f_4-\frac{1}{2}J{\mathrm{\&tau;}}_5^2,f=f_4,t_4\&le;t\&le;t_5\\ f_5-D{\mathrm{\&tau;}}_6,f_5=f_4-\frac{1}{2}J{T}_5^2,t_4\&le;t\&le;t_6\\ f_6-D{\mathrm{\&tau;}}_7+\frac{1}{2}J{\mathrm{\&tau;}}_7^2,f_6=f_5-D{T}_6,t_6\&le;t\&le;t_7\end{array}\right.$

The shifted systems (7) of i+1 section machining locus

$l\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{l}_s+v_s{\mathrm{\&tau;}}_1+\frac{1}{2}{a}_s{\mathrm{\&tau;}}_1^2+\frac{1}{6}J{\mathrm{\&tau;}}_1^3,0\&le;t\&le;t_1\\ {\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1{\mathrm{\&tau;}}_2+\frac{1}{2}A{\mathrm{\&tau;}}_1^2,{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=l_s+{\mathrm{<figure-callout\; id="1"\; label="v\; s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">v</figure-callout>}}_s{T}_{}{}_1+\frac{1}{2}{\mathrm{<figure-callout\; id="1"\; label="a\; s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">a</figure-callout>}}_s{T}_{}^{}{}_1^2+\frac{1}{6}\mathrm{<figure-callout\; id="1"\; label="J\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_1^3{,}^{}{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ {\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2{\mathrm{\&tau;}}_3+\frac{1}{2}A{\mathrm{\&tau;}}_3^2-\frac{1}{6}J{\mathrm{\&tau;}}_3^3,{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_2={\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+f_1{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2+\frac{1}{2}\mathrm{<figure-callout\; id="1"\; label="A\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">A</figure-callout>}{T}_{}^{}{}_1^2,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;t_3\\ {\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+{\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3{\mathrm{\&tau;}}_4,{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+f_2{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3+\frac{1}{2}A{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^2-\frac{1}{6}\mathrm{<figure-callout\; id="3"\; label="J\; T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_3^3,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ l_4+f_4{\mathrm{\&tau;}}_5-\frac{1}{6}J{\mathrm{\&tau;}}_5^3,f={\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+f_3{T}_4,t_4\&le;t\&le;t_5\\ l_5+f_5{\mathrm{\&tau;}}_6-\frac{1}{62}D{\mathrm{\&tau;}}_6^2,f_5=l_4+f_4{T}_5-\frac{1}{6}J{T}_5^3,t_5\&le;t\&le;t_6\\ l_6+f_6{\mathrm{\&tau;}}_7-\frac{1}{2}D{\mathrm{\&tau;}}_7^2+\frac{1}{6}J{\mathrm{\&tau;}}_7^2,f_6=l_5+f_5{T}_6-\frac{1}{2}D{T}_6^2,t_6\&le;t\&le;t_7\end{array}\right.$

Wherein, t is time coordinate, t _i(i=1,2,3 ..., 7) and be the time coordinate at each stage end, τ _iExpression local time is to deduct τ with time t in each stage _iThe time value that obtains, T _i(i=1,2,3 ..., 7) and represent the time span that each stage continues, A is peak acceleration, and D is maximum deceleration, and J is maximum acceleration;

The speed planning processing unit, the acceleration system of equations (5), rate equation group (6) and the shifted systems (7) that are used for obtaining according to stage system of equations acquiring unit carry out the planning of S type curve speed to i+1 section machining locus.

Wherein, the speed planning processing unit comprises:

Interval differentiation subelement is used for calculating the time span that each stage continues, and obtains according to acceleration system of equations (5):

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=\frac{A-a_s}{J},$ ${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3=\frac{A}{J},$ $T_5=\frac{D}{J},$ $T_7=\frac{D-a_e}{J},$

Wherein, T ₁The time span that continues for adding boost phase, T ₃The time span that continues for subtracting boost phase, T ₅Be lasting time span of acceleration and deceleration stage, T ₇For subtracting the time span that the decelerating phase continues;

Reach speed f at even boost phase end ₃, according to rate equation group (6) and shifted systems (7), obtain:

f ₃=f （8）；

${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\frac{f-v_s}{A}-\frac{A}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2\mathrm{AJ}}---\left(9\right);$

Wherein, f is speed of feed, T ₂For the lasting time span of even boost phase, if T ₂﹤ 0, passes through formula $A=\mathrm{sgn}\left(A\right)\sqrt{J-(f-v_s)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2}}---\left(10\right)$

The value of adjusting peak acceleration A is the maximum possible value, and substitution formula (9) recomputates T ₂Value;

Reach speed v subtracting decelerating phase end _e, according to rate equation group (6) and shifted systems (7), obtain:

$T_6=\frac{f-v_e}{D}-\frac{D}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2\mathrm{DJ}}---\left(11\right)$

Wherein, T ₆For lasting time span of even decelerating phase, if T ₆﹤ 0, passes through formula

$D=\mathrm{sgn}\left(D\right)\sqrt{J(f-v_e)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2}}---\left(12\right)$

The value of adjusting maximum deceleration D is the maximum possible value, and substitution formula (11) is counted T again ₆Value

With T ₁, T ₂, T ₃, T ₅, T ₆, T ₇Value substitution rate equation group (6), in conjunction with $L=\underset{k=1}{\overset{7}{\mathrm{\&Sigma;}}}{l}_k-l_{k-1}=l_7-l_s,$ Can get:

$T_4=\frac{1}{f}(\frac{v_e{a}_e+v_s{a}_s}{J}-\frac{a_{\mathrm{<figure-callout\; id="3"\; label="e"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^3+a_{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^3}{3J^2})-$

$\frac{1}{f}[\frac{1}{2A+2\mathrm{<figure-callout\; id="2"\; label="D\; f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">D</figure-callout>}}{f}^{}{}^2+(\frac{A}{2J}+\frac{D}{2J})f+\frac{A(v_s-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2J})}{2J}+\frac{D(v_e-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2J})}{2J}-\frac{{(v_s-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2J})}^2}{2A}-\frac{(v_e-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2J})}{2D}]$

Wherein, T ₄Be the length of duration in stage at the uniform velocity, L is the length of i+1 section machining locus, l ₇For subtracting displacement corresponding to decelerating phase, l _sBe initial position, if T ₄﹤ 0, and the value of adjusting speed of feed f makes T ₄=0, and recomputate T ₁, T ₂, T ₃, T ₅, T ₆And T ₇Value;

The real-time interpolation subelement is used for differentiating according to the interval T that subelement obtains ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value S type curve carried out real-time interpolation calculate.

For solving the problems of the technologies described above, another aspect of the present invention is: a kind of numerically-controlled machine is provided, and this numerically-controlled machine comprises above-mentioned any acceleration/deceleration control device.

The invention has the beneficial effects as follows: the situation that is different from prior art, the embodiment of the present invention is non-vanishing by the acceleration of controlling the first switching place and the second switching place, acceleration in switching place compared to existing technology is zero, start from scratch acceleration and cause long problem of acceleration time at boost phase, the present invention can shorten the acceleration time, improve working (machining) efficiency, less with the brief acceleration saltus step, can reduce the impact to lathe.

Description of drawings

In order to be illustrated more clearly in the technical scheme in the embodiment of the present invention, during the below will describe embodiment, the accompanying drawing of required use is done to introduce simply, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is the schematic flow sheet of Acceleration-deceleration Control Method one embodiment of the present invention;

Fig. 2 calculates the speed v of the first switching place in Acceleration-deceleration Control Method one embodiment of the present invention _sSpeed v with the second switching place _eThe schematic flow sheet of value range;

Fig. 3 is the first switching angle α that obtains the i section machining locus that is connected with i+1 section machining locus by the first switching place and i+1 section machining locus in Acceleration-deceleration Control Method one embodiment of the present invention ₁And the second angle α that transfers of the i+2 section machining locus that is connected with i+1 section machining locus by the second switching place and i+1 section machining locus ₂The schematic diagram of one embodiment;

Fig. 4 is according to the speed v of the first switching place in Acceleration-deceleration Control Method one embodiment of the present invention _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe schematic flow sheet of maximum possible value;

Fig. 5 calculates according to formula (1) and formula (2) the initial acceleration a that obtains i+1 section machining locus in Acceleration-deceleration Control Method one embodiment of the present invention _sThe schematic diagram of possible maximal value one embodiment;

Fig. 6 calculates according to formula (3) and formula (4) the terminal point acceleration a that obtains i+1 section machining locus in Acceleration-deceleration Control Method one embodiment of the present invention _eThe schematic diagram of possible maximal value one embodiment;

Fig. 7 is according to the speed v of the first switching place in Acceleration-deceleration Control Method one embodiment of the present invention _s, the second switching place speed v _e, i+1 section machining locus initial acceleration a _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the non-vanishing schematic flow sheet of acceleration of the first switching place and the second switching place;

Fig. 8 carries out the schematic flow sheet of S type curve speed planning to i+1 section machining locus according to acceleration system of equations (5), rate equation group (6) and shifted systems (7) in Acceleration-deceleration Control Method one embodiment of the present invention;

Fig. 9 is acceleration/deceleration control device one example structure schematic diagram of the present invention;

Figure 10 is the structural representation of the switching place speed calculation module in acceleration/deceleration control device shown in Figure 9;

Figure 11 is the structural representation of the acceleration calculation module in acceleration/deceleration control device shown in Figure 9;

Figure 12 is the structural representation of the speed planning module of acceleration/deceleration control device shown in Figure 9;

Figure 13 is the structural representation of speed planning processing unit of the speed planning module of acceleration/deceleration control device shown in Figure 12; And

Figure 14 is the structural representation of numerically-controlled machine one embodiment of the present invention.

Embodiment

Below in conjunction with the accompanying drawing in embodiment of the present invention, the technical scheme in embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiments.Based on the embodiment in the present invention, those of ordinary skills all belong to the scope of protection of the invention not making the every other embodiment that obtains under the creative work prerequisite.

See also Fig. 1, Fig. 1 is the schematic flow sheet of Acceleration-deceleration Control Method one embodiment of the present invention.This Acceleration-deceleration Control Method comprises:

Step S11: the speed v of calculating the first switching place _sSpeed v with the second switching place _eValue range.

In digital control system processing, the program of each part to be processed is comprised of a plurality of program segments, and these program segments are generally straight line and circular arc, therefore between different straight lines and straight line, between straight line and circular arc, all have switching place between different circular arc and circular arc, i.e. flex point.Particularly, i+1 section machining locus is the machining locus of one of them program segment, and i+1 section machining locus can be any one of straight line or circular arc.When i+1 section machining locus is initial manufacture track in a plurality of program segments, the speed v of the first switching place _sBe zero; When i+1 section machining locus is latter end machining locus in a plurality of program segments, the speed v of the second switching place _eBe zero; When i+1 section machining locus was non-initial manufacture track and latter end machining locus, i+1 section machining locus was between two switchings place (the first switching place and the second switching place), and in the present embodiment, the first switching place speed v _sWith the second switching place speed v _eAll non-vanishing.

Step S12: according to the speed v of the first switching place _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value.

Wherein, in the present embodiment, the initial acceleration a of i+1 section machining locus _sEquate the terminal point acceleration a of i+1 section machining locus with the terminal point acceleration of i section machining locus _eEquate with the initial acceleration of i+2 section machining locus.

Step S13: according to the speed v of the first switching place _s, the second switching place speed v _e, i+1 section machining locus initial acceleration a _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the acceleration of the first switching place and the second switching place is non-vanishing.

By obtaining the speed v of the first switching place _s, the second switching place speed v _e, i+1 section machining locus initial acceleration a _sWith terminal point acceleration a _eThe maximum possible value in conjunction with the length L of i+1 section machining locus with add the speed of feed f in man-hour i+1 section machining locus is carried out the planning of S type curve, wherein, speed of feed f initial value is given by the user, but can make corresponding adjustment according to actual conditions in process.

See also Fig. 2, calculate the speed v of the first switching place in Acceleration-deceleration Control Method one embodiment of the present invention _sSpeed v with the second switching place _eValue range comprise following substep:

Substep S111: the first switching angle α that obtains the i section machining locus that is connected with i+1 section machining locus by the first switching place and i+1 section machining locus ₁, and the second switching angle α that obtains the i+2 section machining locus that is connected with i+1 section machining locus by the second switching place and i+1 section machining locus ₂

Please in conjunction with consulting Fig. 3, adjacent i section machining locus, i+1 section machining locus and i+2 section machining locus are by the first switching place E _iWith the second switching place E _i+1Be connected, i section machining locus and i+1 section machining locus first the switching angle be α ₁, along the unit tangent vector of processing direction of feed i section machining locus be

The unit tangent vector of i+1 section machining locus is

Pass through formula

α 1 ∈ [0 °, 180 °] can obtain α ₁Value.Similarly, second of i+1 section machining locus and i+2 section machining locus the switching angle be α ₂, at the second switching angle α ₂The place along the unit tangent vector of processing direction of feed i+1 section machining locus is

The unit tangent vector of i+2 section machining locus is

Pass through formula α ₂∈ [0 °, 180 °] can obtain α ₂Value.

Wherein, in the present embodiment, line style to i section machining locus, i+1 section machining locus and i+2 section machining locus is not construed as limiting, and the line style of i section machining locus, i+1 section machining locus and i+2 section machining locus can be respectively any one in the line styles such as straight line, circular arc.

Substep S112: according to the first switching angle α ₁With the second switching angle α ₂Calculate respectively the speed v of the first switching place _sSpeed v with the second switching place _eValue range.

Please continue to consult Fig. 3, the moment linear velocity in the same size in actual process before and after General Requirements switching place is located at the first switching place E _iThe speed of front (i section machining locus terminal point) is The first switching place E _iThe speed of (i+1 section machining locus starting point) is afterwards Interpolation cycle is T, and the formula of the acceleration of switching process is:

$\stackrel{\&RightArrow;}{a_{i,i+1}}=\frac{\stackrel{\&RightArrow;}{v_s}-\stackrel{\&RightArrow;}{v_i}}{T}---\left(a\right),$ Wherein $\left|\stackrel{\&RightArrow;}{v_i}\right|=\left|\stackrel{\&RightArrow;}{v_s}\right|$

It is a that lathe allows peak acceleration _max, for convenience of calculation, with the restrictive condition of resultant acceleration as acceleration, the acceleration limit principle of assigning on each motor shaft is identical, does not calculate at this.The condition that does not cause the speed conflict is:

a _i,i+1≤a _max

(a) can obtain according to formula:

$2{\left|\stackrel{\&RightArrow;}{v_i}\right|}^2-2{\left|\stackrel{\&RightArrow;}{v_i}\right|}^2\cos {\mathrm{\&alpha;}}_1\&le;{\left(a_{\max }T\right)}^2$

Solve $\left|\stackrel{\&RightArrow;}{v_s}\right|=\left|\stackrel{\&RightArrow;}{v_i}\right|\&le;\frac{a_{\max }T}{\sqrt{2(1-\cos {\mathrm{\&alpha;}}_1)}};$

Similarly, be located at the second switching place E _i+1The speed of front (i+1 section machining locus terminal point) is

The second switching place E _i+1The speed of (i+2 section machining locus starting point) is afterwards

Interpolation cycle is T, and the formula of the acceleration of switching process is:

$\stackrel{\&RightArrow;}{a_{i+1,i+2}}=\frac{\stackrel{\&RightArrow;}{v_{i+2}}-\stackrel{\&RightArrow;}{v_e}}{T}---\left(b\right),$ Wherein $\left|\stackrel{\&RightArrow;}{v_{i+2}}\right|=\left|\stackrel{\&RightArrow;}{v_e}\right|$

It is a that lathe allows peak acceleration _max, for convenience of calculation, with the restrictive condition of resultant acceleration as acceleration, the acceleration limit principle of assigning on each motor shaft is identical, does not calculate at this.The condition that does not cause the speed conflict is:

a _i+1,i+2≤a _max

(b) can obtain according to formula:

$2{\left|\stackrel{\&RightArrow;}{v_e}\right|}^2-2{\left|\stackrel{\&RightArrow;}{v_e}\right|}^2\cos {\mathrm{\&alpha;}}_2\&le;{\left(a_{\max }T\right)}^2$

Solve $\left|\stackrel{\&RightArrow;}{v_e}\right|=\left|\stackrel{\&RightArrow;}{v_{i+2}}\right|\&le;\frac{a_{\max }T}{\sqrt{2(1-\cos {\mathrm{\&alpha;}}_2)}};$

See also Fig. 4, in Acceleration-deceleration Control Method one embodiment of the present invention according to the speed v of the first switching place _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value comprise following substep:

Substep S211: calculate the initial acceleration a that obtains i+1 section machining locus by formula (1) and formula (2) _sThe maximum possible value.

Please in conjunction with consulting Fig. 5, in order to set forth conveniently, below adjacent machining locus describe with the situation of straight line with the straight line switching, other curves switching types use curve in the tangent line calculating of switching place, can be converted into equally the switching of straight line and straight line.

Last interpolation cycle of i section machining locus is called the i step, and its speed and acceleration are respectively

With

Wherein, last interpolation cycle just in time reaches the terminal point of i section machining locus; An interpolation cycle is called the i+1 step afterwards, the switching from i section machining locus terminal point along i+1 section machining locus direction, and its speed and acceleration are

With

Be the i+2 step at the interpolation cycle of i+1 after the step, its acceleration is

Direction is identical with the tangential direction of i+1 section machining locus.I goes on foot in the interpolation of i+2 step, the relation of acceleration as shown in Figure 5, wherein Be by

With

Poor the decision, due to With

With Corner dimension identical, also namely with

With

Angle identical.

Can be according to formula (1) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2={\left|\stackrel{\&RightArrow;}{a_i}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_i}\right|\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}$ And formula (2) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_1}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_a}\right|\sin {\mathrm{\&alpha;}}_1}{2T}$ Obtain a _iPossible maximal value, particularly, the acceleration before switching place: $\left|\frac{\stackrel{\&RightArrow;}{a_{i+1}}-\stackrel{\&RightArrow;}{a_i}}{T}\right|\&le;J_{\max }---\left(c\right)$

Wherein, J _maxBe maximum acceleration.(c) gets equal sign when formula, namely

The time, can obtain

Maximal value, by the triangle cosine law, obtain formula (1)

${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2={\left|\stackrel{\&RightArrow;}{a_i}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_i}\right|\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}$

Obtain according to formula (1) The derivation formula of size

$\left|\stackrel{\&RightArrow;}{a_i}\right|=\frac{2\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}+\sqrt{{\left(2\right|\stackrel{\&RightArrow;}{a_{i+1}}\left|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}\right)}^2}-4{\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2}{2}---\left(d\right)$

In order to improve working (machining) efficiency, get

Larger solution.Whether the below exists the solution of formula (d) is discussed:

When

The Shi Congdi i step is minimum to the increment size of i+1 step transition brief acceleration, can get $\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}=\stackrel{\&RightArrow;}{a_{i+1}}-\stackrel{\&RightArrow;}{a_i},$ ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}_{\min }=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&alpha;}}{2},$ In conjunction with $\stackrel{\&RightArrow;}{a_{i+1}}T=\stackrel{\&RightArrow;}{v_i}-\stackrel{\&RightArrow;}{v_{i+1}},$ $\left|\stackrel{\&RightArrow;}{v_i}\right|=\left|\stackrel{\&RightArrow;}{v_{i+1}}\right|$ Can obtain:

$\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|=\frac{\sqrt{{|\stackrel{\&RightArrow;}{v_i}-\stackrel{\&RightArrow;}{v_{i+1}}|}^2}}{T}=\frac{\sqrt{{\stackrel{\&RightArrow;}{v_i}}^2-2\left|\stackrel{\&RightArrow;}{v_i}\right|\left|\stackrel{\&RightArrow;}{v_{i+1}}\right|\cos {\mathrm{\&alpha;}}_1+{\stackrel{\&RightArrow;}{v_{i+1}}}^2}}{T}=\frac{\left|\stackrel{\&RightArrow;}{v_i}\right|\sin \frac{{\mathrm{\&alpha;}}_1}{2}}{T}$

Further derive:

$\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_1}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_i}\right|\sin {\mathrm{\&alpha;}}_1}{2T}---\left(2\right)$

Formula (2) substitution formula (d) can be tried to achieve a _iValue, the initial acceleration a of i+1 section machining locus _sWith a _iValue equate.

If the solution of formula (d) does not exist, need to readjust

With

Value, wherein,

Value be v _sValue, make $J_{\max }T=\frac{\left|\stackrel{\&RightArrow;}{v_i}\right|\sin {\mathrm{\&alpha;}}_1}{2T};$

Thereby obtain a _iThe maximum possible value, the also i.e. initial acceleration a of i+1 section machining locus _sThe maximum possible value.

Substep S212: calculate the terminal point acceleration a that obtains i+1 section machining locus by formula (3) and formula (4) _ePossible maximal value.

See also Fig. 6, with the initial acceleration a that calculates i+1 section machining locus _sPossible maximal value similar, describe as an example of the switching of straight line and straight line example equally.

Last interpolation cycle of i+1 section machining locus is called the i+1 step, and its speed and acceleration are respectively With

Wherein, last interpolation cycle just in time arrives the terminal point of i+1 section machining locus; An interpolation cycle is called the i+2 step afterwards, the switching from i+1 section machining locus along i+2 section machining locus direction, and its speed and acceleration are respectively

With

Direction as shown in Figure 6; Be the i+3 step at the interpolation cycle of i+2 after the step, its acceleration is

Direction is identical with the tangential direction of i+2 section machining locus.I+1 goes on foot in the interpolation of i+2 step, the relation of acceleration as shown in Figure 6, wherein

Be by

With

Poor the decision, due to

With

With Corner dimension identical, also namely with With

Angle identical.

Can be according to formula (3) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|}^2={\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_2}{2}$ And formula (4) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|=\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{{\mathrm{\&alpha;}}_2}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_{a+1}}\right|\sin {\mathrm{\&alpha;}}_2}{2T}$ Obtain a _i+1Possible maximal value, its procurement process with obtain a _iPossible peaked computation process similar, be not described in detail in this.Wherein, a _eMaximum possible value and a _i+1Possible maximal value equate.

See also Fig. 7, in Acceleration-deceleration Control Method one embodiment of the present invention according to the speed v of the first switching place _s, the second switching place speed v _e, i+1 section machining locus initial acceleration a _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus carried out S type curve speed planning comprise following substep so that the acceleration of the first switching place and the second switching place is non-vanishing:

Substep S311: according to the initial acceleration a of i+1 section machining locus _s, terminal point acceleration a _e, the first switching place speed v _sAnd the speed v of the second switching place _eWith i+1 section machining locus be divided into acceleration, even acceleration, subtract acceleration, at the uniform velocity, acceleration and deceleration, even deceleration and seven stages and obtain respectively acceleration system of equations (5), rate equation group (6) and shifted systems (7) of slowing down.

Wherein, the acceleration system of equations (5) of i+1 section machining locus:

$a\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}J{\mathrm{\&tau;}}_1+a_s,0\&le;t\&le;t_1\\ A,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ A-J{\mathrm{\&tau;}}_3,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\\ 0,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ -J{\mathrm{\&tau;}}_5,t_4\&le;t\&le;t_5\\ -D,t_5\&le;t\&le;t_6\\ -D+J{\mathrm{\&tau;}}_7,t_6\&le;t\&le;t_7\end{array}\right.$

The rate equation group (6) of i+1 section machining locus:

$f\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{f}_s+a_s{\mathrm{\&tau;}}_1+\frac{1}{2}J{\mathrm{\&tau;}}_1^2,0\&le;t\&le;t_1\\ {\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{\&tau;}}_2,{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=f_s+a_{\mathrm{<figure-callout\; id="1"\; label="s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}{T}_{}{}_1+\frac{1}{2}\mathrm{<figure-callout\; id="1"\; label="J\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_1^2,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+A{\mathrm{\&tau;}}_3=\frac{1}{2}J{\mathrm{\&tau;}}_3^2,{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;t_3\\ {\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3,f={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+{\mathrm{AT}}_3-\frac{1}{2}\mathrm{<figure-callout\; id="3"\; label="J\; T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_3^2,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ f_4-\frac{1}{2}J{\mathrm{\&tau;}}_5^2,f=f_4,t_4\&le;t\&le;t_5\\ f_5-D{\mathrm{\&tau;}}_6,f_5=f_4-\frac{1}{2}J{T}_5^2,t_4\&le;t\&le;t_6\\ f_6-D{\mathrm{\&tau;}}_7+\frac{1}{2}J{\mathrm{\&tau;}}_7^2,f_6=f_5-D{T}_6,t_6\&le;t\&le;t_7\end{array}\right.$

The shifted systems (7) of i+1 section machining locus

$l\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{l}_s+v_s{\mathrm{\&tau;}}_1+\frac{1}{2}{a}_s{\mathrm{\&tau;}}_1^2+\frac{1}{6}J{\mathrm{\&tau;}}_1^3,0\&le;t\&le;t_1\\ l_1+f_1{\mathrm{\&tau;}}_2+\frac{1}{2}A{\mathrm{\&tau;}}_1^2,l_1=l_s+v_s{T}_1+\frac{1}{2}{a}_s{T}_1^2+\frac{1}{6}J{T}_1^3{,}^{}{t}_1\&le;t\&le;t_2\\ l_2+f_2{\mathrm{\&tau;}}_3+\frac{1}{2}A{\mathrm{\&tau;}}_3^2-\frac{1}{6}J{\mathrm{\&tau;}}_3^3,l_2=l_1+f_1{T}_2+\frac{1}{2}A{T}_1^2,t_2\&le;t\&le;t_3\\ l_3+f_3{\mathrm{\&tau;}}_4,l_3=l_2+f_2{T}_3+\frac{1}{2}A{T}_3^2-\frac{1}{6}J{T}_3^3,t_3\&le;t\&le;t_4\\ l_4+f_4{\mathrm{\&tau;}}_5-\frac{1}{6}J{\mathrm{\&tau;}}_5^3,f=l_3+f_3{T}_4,t_4\&le;t\&le;t_5\\ l_5+f_5{\mathrm{\&tau;}}_6-\frac{1}{62}D{\mathrm{\&tau;}}_6^2,f_5=l_4+f_4{T}_5-\frac{1}{6}J{T}_5^3,t_5\&le;t\&le;t_6\\ l_6+f_6{\mathrm{\&tau;}}_7-\frac{1}{2}D{\mathrm{\&tau;}}_7^2+\frac{1}{6}J{\mathrm{\&tau;}}_7^2,f_6=l_5+f_5{T}_6-\frac{1}{2}D{T}_6^2,t_6\&le;t\&le;t_7\end{array}\right.$

The acquisition of above-mentioned system of equations is based on initial and the terminal point acceleration is zero S type curve speed planning theory, its difference is that the initial and terminal point acceleration of above-mentioned system of equations is all non-vanishing, in view of being known by those skilled in the art by zero S type curve speed planning theory based on initial and terminal point acceleration, therefore the derivation of above-mentioned system of equations is not described further.

Wherein, t is time coordinate, t _i(i=1,2,3 ..., 7) and be the time coordinate at each stage end, τ _iExpression local time is to deduct τ with time t in each stage _iThe time value that obtains, T _i(i=1,2,3 ..., 7) and represent the time span that each stage continues, A is peak acceleration, and D is maximum deceleration, and J is maximum acceleration.

Substep S312: i+1 section machining locus is carried out the planning of S type curve speed according to acceleration system of equations (5), rate equation group (6) and shifted systems (7).

Can learn acceleration, speed and each duration in stage of each time point in process and the shift length that travels by above-mentioned system of equations, therefore, be easy to the parameter that obtains according to above-mentioned system of equations i+1 section machining locus is carried out the planning of S type curve speed.Its detailed process is as follows:

See also Fig. 8, according to acceleration system of equations (5), rate equation group (6) and shifted systems (7), the substep that i+1 section machining locus carries out the planning of S type curve speed comprised in Acceleration-deceleration Control Method one embodiment of the present invention:

Substep S3121: the time span that each stage continues is calculated in interval differentiation.

Obtain according to acceleration system of equations (5):

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=\frac{A-a_s}{J},$ ${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3=\frac{A}{J},$ $T_5=\frac{D}{J},$ $T_7=\frac{D-a_e}{J},$

Wherein, T ₁The time span that continues for adding boost phase, T ₃The time span that continues for subtracting boost phase, T ₅Be lasting time span of acceleration and deceleration stage, T ₇For subtracting the time span that the decelerating phase continues;

Reach speed f at even boost phase end ₃, according to rate equation group (6) and shifted systems (7), obtain:

f ₃=f （8）；

${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\frac{f-v_s}{A}-\frac{A}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2\mathrm{AJ}}---\left(9\right);$

Wherein, f is speed of feed, T ₂For the lasting time span of even boost phase, if T ₂﹤ 0, passes through formula $A=\mathrm{sgn}\left(A\right)\sqrt{J-(f-v_s)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2}}---\left(10\right)$

The value of adjusting peak acceleration A is the maximum possible value, and substitution formula (9) recomputates T ₂Value;

Reach speed v subtracting decelerating phase end _e, according to rate equation group (6) and shifted systems (7), obtain:

$T_6=\frac{f-v_e}{D}-\frac{D}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2\mathrm{DJ}}---\left(11\right)$

Wherein, T ₆For lasting time span of even decelerating phase, if T ₆﹤ 0, passes through formula

$D=\mathrm{sgn}\left(D\right)\sqrt{J(f-v_e)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2}}---\left(12\right)$

The value of adjusting maximum deceleration D is the maximum possible value, and substitution formula (11) is counted T again ₆Value;

With T ₁, T ₂, T ₃, T ₅, T ₆, T ₇Value substitution rate equation group (6), in conjunction with $L=\underset{k=1}{\overset{7}{\mathrm{\&Sigma;}}}{l}_k-l_{k-1}=l_7-l_s,$ Can get:

$T_4=\frac{1}{f}(\frac{v_e{a}_e+v_s{a}_s}{J}-\frac{a_{\mathrm{<figure-callout\; id="3"\; label="e"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^3+a_{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^3}{3J^2})-$

$\frac{1}{f}[\frac{1}{2A+2\mathrm{<figure-callout\; id="2"\; label="D\; f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">D</figure-callout>}}{f}^{}{}^2+(\frac{A}{2J}+\frac{D}{2J})f+\frac{A(v_s-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2J})}{2J}+\frac{D(v_e-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2J})}{2J}-\frac{{(v_s-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2J})}^2}{2A}-\frac{(v_e-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2J})}{2D}]$

Wherein, T ₄Be the length of duration in stage at the uniform velocity, L is the length of i+1 section machining locus, l ₇For subtracting displacement corresponding to decelerating phase, l _sBe initial position, if T ₄﹤ 0, and the value of adjusting speed of feed f makes T ₄=0, and recomputate T ₁, T ₂, T ₃, T ₅, T ₆And T ₇Value;

It should be noted that also needs the value of peak acceleration A and maximum deceleration D is adjusted accordingly when adjusting the value of speed of feed f.

Substep S3122: according to lasting time span T of stage ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value S type curve carried out real-time interpolation calculate.

Obtain T by said method ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value after, the time span that continues according to each stage and transition point time carry out real-time interpolation to S type curve and calculate.

The Acceleration-deceleration Control Method of the embodiment of the present invention is by the speed v in the first switching place _sSpeed v with the second switching place _eObtain maximum initial acceleration and the maximum terminal point acceleration of the i+1 section machining locus that allows in scope, thereby i+1 section machining locus is carried out the planning of S type curve speed, make in process the acceleration of the first switching place and the second switching place non-vanishing.Be zero situation compared to existing technology at the acceleration of switching place, the Acceleration-deceleration Control Method of the embodiment of the present invention can effectively improve working (machining) efficiency, reduces in process the impact to lathe.

See also Fig. 9, Fig. 9 is acceleration/deceleration control device one example structure schematic diagram of the present invention.S type curve is used for the i+1 section machining locus between the first switching place and the second switching place is carried out speed planning, and this acceleration/deceleration control device comprises switching place speed calculation module 11, acceleration calculation module 12 and speed planning module 13.

Switching place speed calculation module 11 is used for calculating the speed v of the first switching place _sSpeed v with the second switching place _eValue range.When i+1 section machining locus is initial manufacture track in a plurality of program segments, the speed v of the first switching place _sBe zero; When i+1 section machining locus is latter end machining locus in a plurality of program segments, the speed v of the second switching place _eBe zero; When i+1 section machining locus was non-initial manufacture track and latter end machining locus, i+1 section machining locus was between two switchings place (the first switching place and the second switching place), and in the present embodiment, the first switching place speed v _sWith the second switching place speed v _eAll non-vanishing.

Particularly, see also Figure 10, this switching place speed calculation module 11 comprises switching angle acquiring unit 111 and speed computing unit 112.

Switching angle acquiring unit 111 is used for obtaining first of the i section machining locus that is connected with i+1 section machining locus by the first switching place and the i+1 section machining locus angle α that transfers ₁, and the second switching angle α that obtains the i+2 section machining locus that is connected with i+1 section machining locus by the second switching place and i+1 section machining locus ₂

Speed computing unit 112 is for the first switching angle α that obtains according to the angle acquiring unit of transferring ₁With the second switching angle α ₂Calculate respectively the speed v of the first switching place _sSpeed v with the second switching place _eValue range.

Acceleration calculation module 12 is used for calculating the speed v of the first switching place that obtains according to switching place speed calculation module 11 _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value.

Particularly, see also Figure 11, this acceleration calculation module 12 comprises initial acceleration computing unit 121 and terminal point acceleration calculation unit 122.

Initial acceleration computing unit 121 is used for according to formula (1)

${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2={\left|\stackrel{\&RightArrow;}{a_i}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_i}\right|\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}$ And

Formula (2) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_1}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_a}\right|\sin {\mathrm{\&alpha;}}_1}{2T}$

Obtain a _iThe maximum possible value, a _iValue and the initial acceleration a of i+1 section machining locus _sEquate, wherein,

Be acceleration corresponding to last interpolation cycle T of i section machining locus,

Be the acceleration of the first switching place, the position that last interpolation cycle T machining of i section machining locus arrives is the terminal point of i section machining locus.

Terminal point acceleration calculation unit 122 is used for according to formula (3)

${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|}^2={\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_2}{2}$ And

Formula (4) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_2}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_{a+1}}\right|\sin {\mathrm{\&alpha;}}_2}{2T}$

Obtain a _i+1The maximum possible value, a _i+1Value and the terminal point acceleration a of i+1 section machining locus _eEquate, wherein,

Be acceleration corresponding to last interpolation cycle T of i+1 section machining locus,

Be the acceleration of the first switching place, the position that last interpolation cycle T machining of i+1 section machining locus arrives is the terminal point of i+1 section machining locus.

Speed planning module 13 is used for calculating the speed v of the first switching place that obtains according to switching place speed calculation module 11 _sSpeed v with the second switching place _eValue range and the acceleration calculation module obtain 12 the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the acceleration of described the first switching place and described the second switching place is non-vanishing.

Particularly, see also Figure 12, this speed planning module 13 comprises stage system of equations acquiring unit 131 and speed planning processing unit 132.

The initial acceleration a that stage system of equations acquiring unit 131 is used for according to i+1 section machining locus _s, terminal point acceleration a _e, the first switching place speed v _sAnd the speed v of the second switching place _eWith i+1 section machining locus be divided into acceleration, even acceleration, subtract acceleration, at the uniform velocity, acceleration and deceleration, even deceleration and seven stages and obtain respectively following system of equations of slowing down:

The acceleration system of equations (5) of i+1 section machining locus:

$a\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}J{\mathrm{\&tau;}}_1+a_s,0\&le;t\&le;t_1\\ A,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ A-J{\mathrm{\&tau;}}_3,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\\ 0,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ -J{\mathrm{\&tau;}}_5,t_4\&le;t\&le;t_5\\ -D,t_5\&le;t\&le;t_6\\ -D+J{\mathrm{\&tau;}}_7,t_6\&le;t\&le;t_7\end{array}\right.$

The rate equation group (6) of i+1 section machining locus:

$f\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{f}_s+a_s{\mathrm{\&tau;}}_1+\frac{1}{2}J{\mathrm{\&tau;}}_1^2,0\&le;t\&le;t_1\\ {\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{\&tau;}}_2,{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=f_s+a_{\mathrm{<figure-callout\; id="1"\; label="s\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}{T}_{}{}_1+\frac{1}{2}\mathrm{<figure-callout\; id="1"\; label="J\; T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_1^2,{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;t\&le;t_2\\ {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+A{\mathrm{\&tau;}}_3=\frac{1}{2}J{\mathrm{\&tau;}}_3^2,{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+A{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\&le;t\&le;t_3\\ {\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3,f={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+{\mathrm{AT}}_3-\frac{1}{2}\mathrm{<figure-callout\; id="3"\; label="J\; T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">J</figure-callout>}{T}_{}^{}{}_3^2,{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\&le;t\&le;t_4\\ f_4-\frac{1}{2}J{\mathrm{\&tau;}}_5^2,f=f_4,t_4\&le;t\&le;t_5\\ f_5-D{\mathrm{\&tau;}}_6,f_5=f_4-\frac{1}{2}J{T}_5^2,t_4\&le;t\&le;t_6\\ f_6-D{\mathrm{\&tau;}}_7+\frac{1}{2}J{\mathrm{\&tau;}}_7^2,f_6=f_5-D{T}_6,t_6\&le;t\&le;t_7\end{array}\right.$

The shifted systems (7) of i+1 section machining locus

$l\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{l}_s+v_s{\mathrm{\&tau;}}_1+\frac{1}{2}{a}_s{\mathrm{\&tau;}}_1^2+\frac{1}{6}J{\mathrm{\&tau;}}_1^3,0\&le;t\&le;t_1\\ l_1+f_1{\mathrm{\&tau;}}_2+\frac{1}{2}A{\mathrm{\&tau;}}_1^2,l_1=l_s+v_s{T}_1+\frac{1}{2}{a}_s{T}_1^2+\frac{1}{6}J{T}_1^3{,}^{}{t}_1\&le;t\&le;t_2\\ l_2+f_2{\mathrm{\&tau;}}_3+\frac{1}{2}A{\mathrm{\&tau;}}_3^2-\frac{1}{6}J{\mathrm{\&tau;}}_3^3,l_2=l_1+f_1{T}_2+\frac{1}{2}A{T}_1^2,t_2\&le;t\&le;t_3\\ l_3+f_3{\mathrm{\&tau;}}_4,l_3=l_2+f_2{T}_3+\frac{1}{2}A{T}_3^2-\frac{1}{6}J{T}_3^3,t_3\&le;t\&le;t_4\\ l_4+f_4{\mathrm{\&tau;}}_5-\frac{1}{6}J{\mathrm{\&tau;}}_5^3,f=l_3+f_3{T}_4,t_4\&le;t\&le;t_5\\ l_5+f_5{\mathrm{\&tau;}}_6-\frac{1}{62}D{\mathrm{\&tau;}}_6^2,f_5=l_4+f_4{T}_5-\frac{1}{6}J{T}_5^3,t_5\&le;t\&le;t_6\\ l_6+f_6{\mathrm{\&tau;}}_7-\frac{1}{2}D{\mathrm{\&tau;}}_7^2+\frac{1}{6}J{\mathrm{\&tau;}}_7^2,f_6=l_5+f_5{T}_6-\frac{1}{2}D{T}_6^2,t_6\&le;t\&le;t_7\end{array}\right.$

Wherein, t is time coordinate, t _i(i=1,2,3 ..., 7) and be the time coordinate at each stage end, τ _iExpression local time is to deduct τ with time t in each stage _iThe time value that obtains, T _i(i=1,2,3 ..., 7) and represent the time span that each stage continues, A is peak acceleration, and D is maximum deceleration, and J is maximum acceleration.

Acceleration system of equations (5), rate equation group (6) and shifted systems (7) that speed planning processing unit 132 is used for obtaining according to stage system of equations acquiring unit 131 carry out the planning of S type curve speed to i+1 section machining locus.Particularly, see also Figure 13, this speed planning processing unit 132 comprises interval differentiate subelement 1321 and real-time interpolation subelement 1322.

Interval differentiation subelement 1321 is used for calculating the time span that each stage continues, and obtains according to acceleration system of equations (5):

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=\frac{A-a_s}{J},$ ${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_3=\frac{A}{J},$ $T_5=\frac{D}{J},$ $T_7=\frac{D-a_e}{J},$

Wherein, T ₁The time span that continues for adding boost phase, T ₃The time span that continues for subtracting boost phase, T ₅Be lasting time span of acceleration and deceleration stage, T ₇For subtracting the time span that the decelerating phase continues;

Reach speed f at even boost phase end ₃, according to rate equation group (6) and shifted systems (7), obtain:

f ₃=f （8）；

${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\frac{f-v_s}{A}-\frac{A}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2\mathrm{AJ}}---\left(9\right);$

Wherein, f is speed of feed, T ₂For the lasting time span of even boost phase, if T ₂﹤ 0, passes through formula $A=\mathrm{sgn}\left(A\right)\sqrt{J-(f-v_s)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2}}---\left(10\right)$

The value of adjusting peak acceleration A is the maximum possible value, and substitution formula (9) recomputates T ₂Value;

Reach speed v subtracting decelerating phase end _e, according to rate equation group (6) and shifted systems (7), obtain:

$T_6=\frac{f-v_e}{D}-\frac{D}{J}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2\mathrm{DJ}}---\left(11\right)$

Wherein, T ₆For lasting time span of even decelerating phase, if T ₆﹤ 0, passes through formula

$D=\mathrm{sgn}\left(D\right)\sqrt{J(f-v_e)+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2}}---\left(12\right)$

The value of adjusting maximum deceleration D is the maximum possible value, and substitution formula (11) is counted T again ₆Value

With T ₁, T ₂, T ₃, T ₅, T ₆, T ₇Value substitution rate equation group (6), in conjunction with $L=\underset{k=1}{\overset{7}{\mathrm{\&Sigma;}}}{l}_k-l_{k-1}=l_7-l_s,$ Can get:

$T_4=\frac{1}{f}(\frac{v_e{a}_e+v_s{a}_s}{J}-\frac{a_{\mathrm{<figure-callout\; id="3"\; label="e"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^3+a_{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^3}{3J^2})-$

$\frac{1}{f}[\frac{1}{2A+2\mathrm{<figure-callout\; id="2"\; label="D\; f"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">D</figure-callout>}}{f}^{}{}^2+(\frac{A}{2J}+\frac{D}{2J})f+\frac{A(v_s-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2J})}{2J}+\frac{D(v_e-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2J})}{2J}-\frac{{(v_s-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2J})}^2}{2A}-\frac{(v_e-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002809963600023.png,HDA00002809963600031.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2J})}{2D}]$

Wherein, T ₄Be the length of duration in stage at the uniform velocity, L is the length of i+1 section machining locus, l ₇For subtracting displacement corresponding to decelerating phase, l _sBe initial position, if T ₄﹤ 0, and the value of adjusting speed of feed f makes T ₄=0, and recomputate T ₁, T ₂, T ₃, T ₅, T ₆And T ₇Value.

Real-time interpolation subelement 1322 is used for differentiating according to the interval T that subelement obtains ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value S type curve carried out real-time interpolation calculate.

The acceleration/deceleration control device of the embodiment of the present invention is by the speed v in the first switching place _sSpeed v with the second switching place _eObtain maximum initial acceleration and the maximum terminal point acceleration of the i+1 section machining locus that allows in scope, thereby i+1 section machining locus is carried out the planning of S type curve speed, make in process non-vanishing at the acceleration of the first switching place and the second switching place.Be zero at the acceleration of switching place compared to existing technology, the acceleration/deceleration control device of the embodiment of the present invention can effectively improve working (machining) efficiency, reduces in process the impact to lathe.

See also Figure 14, Figure 14 is the structural representation of numerically-controlled machine one embodiment of the present invention.This numerically-controlled machine comprises control device 60, drive unit 70, actuating unit 80 and supply unit (not shown).

This supply unit is to this numerically-controlled machine power supply, the actuating unit 80 that this control device 60 is controlled these drive unit 70 driving numerically-controlled machines operates, wherein, actuating unit 80 comprises the parts that NC cutting cutter head, NC laser welding head, numerical control operated platform, robot arm etc. can be controlled by software program.Control device 60 includes but not limited to acceleration/deceleration control device 601.Acceleration/deceleration control device 601 is used for the acceleration of switching place of adjacent machining locus is controlled and made it non-vanishing.

In the present embodiment, acceleration/deceleration control device 601 comprises:

Switching place speed calculation module is used for calculating the speed v of the first switching place _sSpeed v with the second switching place _eValue range.

The acceleration calculation module is used for the speed v according to the first switching place of switching place speed calculation module calculating acquisition _sSpeed v with the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value.

The speed planning module is used for the speed v according to the first switching place of switching place speed calculation module calculating acquisition _sSpeed v with the second switching place _eValue range and the initial acceleration a of the i+1 section machining locus that obtains of acceleration calculation module _sWith terminal point acceleration a _eThe maximum possible value i+1 section machining locus is carried out S type curve speed planning so that the acceleration of the first switching place and the second switching place is non-vanishing.

Certainly, its specific works principle includes but not limited to Acceleration-deceleration Control Method and the device that previous embodiment is related, does not repeat them here.

The numerically-controlled machine of the present embodiment is by the speed v in the first switching place _sSpeed v with the second switching place _eObtain maximum initial acceleration and the maximum terminal point acceleration of the i+1 section machining locus that allows in scope, thereby i+1 section machining locus is carried out the planning of S type curve speed, make in process non-vanishing at the acceleration of the first switching place and the second switching place.Be zero at the acceleration of switching place compared to existing technology, the acceleration/deceleration control device of the embodiment of the present invention can effectively improve working (machining) efficiency, reduces in process the impact to lathe.

The above is only embodiments of the present invention; not thereby limit the scope of the claims of the present invention; every equivalent structure or equivalent flow process conversion that utilizes instructions of the present invention and accompanying drawing content to do; or directly or indirectly be used in other relevant technical fields, all in like manner be included in scope of patent protection of the present invention.

Claims (12)

1. Acceleration-deceleration Control Method based on S type curve, described S type curve is used for the i+1 section machining locus between the first switching place and the second switching place is carried out speed planning, it is characterized in that, the acceleration of controlling described the first switching place and described the second switching place is non-vanishing.

2. Acceleration-deceleration Control Method according to claim 1, is characterized in that, the non-vanishing step of acceleration of described the first switching place of described control and described the second switching place specifically comprises:

Calculate the speed v of described the first switching place _sSpeed v with described the second switching place _eValue range;

Speed v according to described the first switching place _sSpeed v with described the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value;

Speed v according to described the first switching place _s, described the second switching place speed v _e, described i+1 section machining locus described initial acceleration a _sWith described terminal point acceleration a _eThe maximum possible value described i+1 section machining locus is carried out S type curve speed planning so that the acceleration of described the first switching place and described the second switching place is non-vanishing.

3. Acceleration-deceleration Control Method according to claim 2, is characterized in that, the speed v of described the first switching place of described calculating _sSpeed v with described the second switching place _eThe step of value range specifically comprise:

Obtain the first switching angle α of the i section machining locus that is connected with described i+1 section machining locus by described the first switching place and described i+1 section machining locus ₁, and the second switching angle α that obtains the i+2 section machining locus that is connected with described i+1 section machining locus by described the second switching place and described i+1 section machining locus ₂

According to described the first switching angle α ₁With described the second switching angle α ₂Calculate respectively the speed v of described the first switching place _sSpeed v with described the second switching place _eValue range.

4. Acceleration-deceleration Control Method according to claim 2, is characterized in that, described speed v according to described the first switching place _sSpeed v with described the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe step of maximum possible value specifically comprise:

According to formula (1) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2={\left|\stackrel{\&RightArrow;}{a_i}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_i}\right|\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}$ And formula (2) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_1}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_a}\right|\sin {\mathrm{\&alpha;}}_1}{2T}$ Obtain a _iPossible maximal value, a _iValue and the initial acceleration a of described i+1 section machining locus _sEquate, wherein,

Be acceleration corresponding to described last interpolation cycle T of i section machining locus, Be the acceleration of described the first switching place, the position that last interpolation cycle T machining of described i section machining locus arrives is the terminal point of described i section machining locus;

According to formula (3) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|}^2={\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_2}{2}$ And formula (4) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|=\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{{\mathrm{\&alpha;}}_2}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_{a+1}}\right|\sin {\mathrm{\&alpha;}}_2}{2T}$ Obtain a _i+1Possible maximal value, a _i+1Value and the terminal point acceleration a of described i+1 section machining locus _eEquate, wherein,

Be acceleration corresponding to described last interpolation cycle T of i+1 section machining locus,

Be the acceleration of described the first switching place, the position that last interpolation cycle T machining of described i+1 section machining locus arrives is the terminal point of described i+1 section machining locus.

5. Acceleration-deceleration Control Method according to claim 2, is characterized in that, described speed v according to described the first switching place _s, described the second switching place speed v _e, described i+1 section machining locus described initial acceleration a _sWith described terminal point acceleration a _eThe maximum possible value described i+1 section machining locus is carried out S type curve speed planning so that the non-vanishing step of the acceleration of described the first switching place and described the second switching place specifically comprises;

Described initial acceleration a according to described i+1 section machining locus _s, described terminal point acceleration a _e, described the first switching place speed v _sAnd the speed v of described the second switching place _eWith described i+1 section machining locus be divided into acceleration, even acceleration, subtract acceleration, at the uniform velocity, acceleration and deceleration, even deceleration and seven stages and obtain respectively following system of equations of slowing down:

The acceleration system of equations (5) of described i+1 section machining locus:

$a\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}J{\mathrm{\&tau;}}_1+a_s,0\&le;t\&le;t_1\\ A,t_1\&le;t\&le;t_2\\ A-J{\mathrm{\&tau;}}_3,t_2\&le;t\&le;t_3\\ 0,t_3\&le;t\&le;t_4\\ -J{\mathrm{\&tau;}}_5,t_4\&le;t\&le;t_5\\ -D,t_5\&le;t\&le;t_6\\ -D+J{\mathrm{\&tau;}}_7,t_6\&le;t\&le;t_7\end{array}\right.$

The rate equation group (6) of described i+1 section machining locus:

$f\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{f}_s+a_s{\mathrm{\&tau;}}_1+\frac{1}{2}J{\mathrm{\&tau;}}_1^2,0\&le;t\&le;t_1\\ f_1+A{\mathrm{\&tau;}}_2,f_1=f_s+a_s{T}_1+\frac{1}{2}J{T}_1^2,t_1\&le;t\&le;t_2\\ f_2+A{\mathrm{\&tau;}}_3=\frac{1}{2}J{\mathrm{\&tau;}}_3^2,f_2=f_1+A{T}_2,t_2\&le;t\&le;t_3\\ f_3,f=f_3=f_2+{\mathrm{AT}}_3-\frac{1}{2}J{T}_3^2,t_3\&le;t\&le;t_4\\ f_4-\frac{1}{2}J{\mathrm{\&tau;}}_5^2,f=f_4,t_4\&le;t\&le;t_5\\ f_5-D{\mathrm{\&tau;}}_6,f_5=f_4-\frac{1}{2}J{T}_5^2,t_4\&le;t\&le;t_6\\ f_6-D{\mathrm{\&tau;}}_7+\frac{1}{2}J{\mathrm{\&tau;}}_7^2,f_6=f_5-D{T}_6,t_6\&le;t\&le;t_7\end{array}\right.$

The shifted systems (7) of described i+1 section machining locus

$l\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{l}_s+v_s{\mathrm{\&tau;}}_1+\frac{1}{2}{a}_s{\mathrm{\&tau;}}_1^2+\frac{1}{6}J{\mathrm{\&tau;}}_1^3,0\&le;t\&le;t_1\\ l_1+f_1{\mathrm{\&tau;}}_2+\frac{1}{2}A{\mathrm{\&tau;}}_1^2,l_1=l_s+v_s{T}_1+\frac{1}{2}{a}_s{T}_1^2+\frac{1}{6}J{T}_1^3{,}^{}{t}_1\&le;t\&le;t_2\\ l_2+f_2{\mathrm{\&tau;}}_3+\frac{1}{2}A{\mathrm{\&tau;}}_3^2-\frac{1}{6}J{\mathrm{\&tau;}}_3^3,l_2=l_1+f_1{T}_2+\frac{1}{2}A{T}_1^2,t_2\&le;t\&le;t_3\\ l_3+f_3{\mathrm{\&tau;}}_4,l_3=l_2+f_2{T}_3+\frac{1}{2}A{T}_3^2-\frac{1}{6}J{T}_3^3,t_3\&le;t\&le;t_4\\ l_4+f_4{\mathrm{\&tau;}}_5-\frac{1}{6}J{\mathrm{\&tau;}}_5^3,f=l_3+f_3{T}_4,t_4\&le;t\&le;t_5\\ l_5+f_5{\mathrm{\&tau;}}_6-\frac{1}{62}D{\mathrm{\&tau;}}_6^2,f_5=l_4+f_4{T}_5-\frac{1}{6}J{T}_5^3,t_5\&le;t\&le;t_6\\ l_6+f_6{\mathrm{\&tau;}}_7-\frac{1}{2}D{\mathrm{\&tau;}}_7^2+\frac{1}{6}J{\mathrm{\&tau;}}_7^2,f_6=l_5+f_5{T}_6-\frac{1}{2}D{T}_6^2,t_6\&le;t\&le;t_7\end{array}\right.$

Wherein, t is time coordinate, t _i(i=1,2,3 ..., 7) and be the time coordinate at each stage end, τ _iExpression local time is to deduct τ with time t in each stage _iThe time value that obtains, T _i(i=1,2,3 ..., 7) and represent the time span that each stage continues, A is peak acceleration, and D is maximum deceleration, and J is maximum acceleration;

According to described acceleration system of equations (5), described rate equation group (6) and described shifted systems (7), described i+1 section machining locus is carried out the planning of S type curve speed.

6. Acceleration-deceleration Control Method according to claim 5, it is characterized in that, describedly according to described acceleration system of equations (5), described rate equation group (6) and described shifted systems (7), the step that described i+1 section machining locus carries out S type curve speed planning is specifically comprised:

Interval differentiation: the described interval time span that each stage of calculating continues of differentiating obtains according to described acceleration system of equations (5):

$T_1=\frac{A-a_s}{J},$ $T_3=\frac{A}{J},$ $T_5=\frac{D}{J},$ $T_7=\frac{D-a_e}{J},$

Wherein, T ₁The time span that continues for adding boost phase, T ₃The time span that continues for subtracting boost phase, T ₅Be lasting time span of acceleration and deceleration stage, T ₇For subtracting the time span that the decelerating phase continues;

Reach speed f at even boost phase end ₃, according to described rate equation group (6) and described shifted systems (7), obtain:

f ₃=f （8）；

$T_2=\frac{f-v_s}{A}-\frac{A}{J}+\frac{a_s^2}{2\mathrm{AJ}}---\left(9\right);$

Wherein, f is speed of feed, T ₂For the lasting time span of even boost phase, if T ₂﹤ 0, passes through formula $A=\mathrm{sgn}\left(A\right)\sqrt{J-(f-v_s)+\frac{a_s^2}{2}}---\left(10\right)$

The value of adjusting peak acceleration A is the maximum possible value, and substitution formula (9) recomputates T ₂Value;

Reach speed v subtracting decelerating phase end _e, according to described rate equation group (6) and described shifted systems (7), obtain:

$T_6=\frac{f-v_e}{D}-\frac{D}{J}+\frac{a_e^2}{2\mathrm{DJ}}---\left(11\right)$

Wherein, T ₆For lasting time span of even decelerating phase, if T ₆﹤ 0, passes through formula

$D=\mathrm{sgn}\left(D\right)\sqrt{J(f-v_e)+\frac{a_e^2}{2}}---\left(12\right)$

The value of adjusting maximum deceleration D is the maximum possible value, and substitution formula (11) is counted T again ₆Value;

With T ₁, T ₂, T ₃, T ₅, T ₆, T ₇Value substitution rate equation group (6), in conjunction with $L=\underset{k=1}{\overset{7}{\mathrm{\&Sigma;}}}{l}_k-l_{k-1}=l_7-l_s,$ Can get:

$T_4=\frac{1}{f}(\frac{v_e{a}_e+v_s{a}_s}{J}-\frac{a_e^3+a_s^3}{3J^2})-$

$\frac{1}{f}[\frac{1}{2A+2D}{f}^2+(\frac{A}{2J}+\frac{D}{2J})f+\frac{A(v_s-\frac{a_s^2}{2J})}{2J}+\frac{D(v_e-\frac{a_e^2}{2J})}{2J}-\frac{{(v_s-\frac{a_s^2}{2J})}^2}{2A}-\frac{(v_e-\frac{a_e^2}{2J})}{2D}]$

Wherein, T ₄Be the length of duration in stage at the uniform velocity, L is the length of i+1 section machining locus, l ₇For subtracting displacement corresponding to decelerating phase, l _sBe initial position, if T ₄﹤ 0, and the value of adjusting speed of feed f makes T ₄=0, and recomputate T ₁, T ₂, T ₃, T ₅, T ₆And T ₇Value;

Real-time interpolation: according to T ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value S type curve carried out real-time interpolation calculate.

7. acceleration/deceleration control device based on S type curve, described S type curve are used for the i+1 section machining locus between the first switching place and the second switching place is carried out speed planning, it is characterized in that, described acceleration/deceleration control device comprises:

Switching place speed calculation module is used for calculating the speed v of described the first switching place _sSpeed v with described the second switching place _eValue range;

The acceleration calculation module is used for the speed v according to described first switching place of described switching place speed calculation module calculating acquisition _sSpeed v with described the second switching place _eValue range calculate the initial acceleration a of i+1 section machining locus _sWith terminal point acceleration a _eThe maximum possible value;

The speed planning module is used for the speed v according to described first switching place of described switching place speed calculation module calculating acquisition _sSpeed v with described the second switching place _eValue range and the initial acceleration a of the described i+1 section machining locus that obtains of described acceleration calculation module _sWith terminal point acceleration a _eThe maximum possible value described i+1 section machining locus is carried out S type curve speed planning so that the acceleration of described the first switching place and described the second switching place is non-vanishing.

8. acceleration/deceleration control device according to claim 7, is characterized in that, described speed calculation module comprises:

Switching angle acquiring unit is used for obtaining first of the i section machining locus that is connected with described i+1 section machining locus by described the first switching place and the described i+1 section machining locus angle α that transfers ₁, and the second switching angle α that obtains the i+2 section machining locus that is connected with described i+1 section machining locus by described the second switching place and described i+1 section machining locus ₂

The speed computing unit is used for described the first switching angle α that obtains according to described switching angle acquiring unit ₁With described the second switching angle α ₂Calculate respectively the speed v of described the first switching place _sSpeed v with described the second switching place _eValue range.

9. acceleration/deceleration control device according to claim 7, is characterized in that, described acceleration calculation module comprises:

The initial acceleration computing unit, described initial acceleration computing unit is used for according to formula (1) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|}^2={\left|\stackrel{\&RightArrow;}{a_i}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_i}\right|\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_1}{2}$ And formula (2) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_i}\right|=\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\cos \frac{{\mathrm{\&alpha;}}_1}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_a}\right|\sin {\mathrm{\&alpha;}}_1}{2T}$ Obtain a _iPossible maximal value, a _iValue and the initial acceleration a of described i+1 section machining locus _sEquate, wherein,

Be acceleration corresponding to described last interpolation cycle T of i section machining locus,

Be the acceleration of described the first switching place, the position that last interpolation cycle T machining of described i section machining locus arrives is the terminal point of described i section machining locus;

Terminal point acceleration calculation unit, described terminal point acceleration calculation unit is used for according to formula (3) ${\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|}^2={\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|}^2+{\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|}^2-2\left|\stackrel{\&RightArrow;}{a_{i+1}}\right|\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{\mathrm{\&pi;}-{\mathrm{\&alpha;}}_2}{2}$ And

Formula (4) $\left|\stackrel{\&RightArrow;}{{\mathrm{\&Delta;a}}_{i+1}}\right|=\left|\stackrel{\&RightArrow;}{a_{i+2}}\right|\cos \frac{{\mathrm{\&alpha;}}_2}{2}=\frac{\left|\stackrel{\&RightArrow;}{v_{a+1}}\right|\sin {\mathrm{\&alpha;}}_2}{2T}$ Obtain a _i+1Possible maximal value, a _i+1Value and the terminal point acceleration a of described i+1 section machining locus _eEquate, wherein,

Be acceleration corresponding to described last interpolation cycle T of i+1 section machining locus,

Be the acceleration of described the first switching place, the position that last interpolation cycle T machining of described i+1 section machining locus arrives is the terminal point of described i+1 section machining locus.

10. acceleration/deceleration control device according to claim 7, is characterized in that, described speed planning module comprises:

Stage system of equations acquiring unit is used for the described initial acceleration a according to described i+1 section machining locus _s, described terminal point acceleration a _e, described the first switching place speed v _sAnd the speed v of described the second switching place _eWith described i+1 section machining locus be divided into acceleration, even acceleration, subtract acceleration, at the uniform velocity, acceleration and deceleration, even deceleration and seven stages and obtain respectively following system of equations of slowing down:

The acceleration system of equations (5) of described i+1 section machining locus:

$a\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}J{\mathrm{\&tau;}}_1+a_s,0\&le;t\&le;t_1\\ A,t_1\&le;t\&le;t_2\\ A-J{\mathrm{\&tau;}}_3,t_2\&le;t\&le;t_3\\ 0,t_3\&le;t\&le;t_4\\ -J{\mathrm{\&tau;}}_5,t_4\&le;t\&le;t_5\\ -D,t_5\&le;t\&le;t_6\\ -D+J{\mathrm{\&tau;}}_7,t_6\&le;t\&le;t_7\end{array}\right.$

The rate equation group (6) of described i+1 section machining locus:

$f\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{f}_s+a_s{\mathrm{\&tau;}}_1+\frac{1}{2}J{\mathrm{\&tau;}}_1^2,0\&le;t\&le;t_1\\ f_1+A{\mathrm{\&tau;}}_2,f_1=f_s+a_s{T}_1+\frac{1}{2}J{T}_1^2,t_1\&le;t\&le;t_2\\ f_2+A{\mathrm{\&tau;}}_3=\frac{1}{2}J{\mathrm{\&tau;}}_3^2,f_2=f_1+A{T}_2,t_2\&le;t\&le;t_3\\ f_3,f=f_3=f_2+{\mathrm{AT}}_3-\frac{1}{2}J{T}_3^2,t_3\&le;t\&le;t_4\\ f_4-\frac{1}{2}J{\mathrm{\&tau;}}_5^2,f=f_4,t_4\&le;t\&le;t_5\\ f_5-D{\mathrm{\&tau;}}_6,f_5=f_4-\frac{1}{2}J{T}_5^2,t_4\&le;t\&le;t_6\\ f_6-D{\mathrm{\&tau;}}_7+\frac{1}{2}J{\mathrm{\&tau;}}_7^2,f_6=f_5-D{T}_6,t_6\&le;t\&le;t_7\end{array}\right.$

The shifted systems (7) of described i+1 section machining locus

$l\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}{l}_s+v_s{\mathrm{\&tau;}}_1+\frac{1}{2}{a}_s{\mathrm{\&tau;}}_1^2+\frac{1}{6}J{\mathrm{\&tau;}}_1^3,0\&le;t\&le;t_1\\ l_1+f_1{\mathrm{\&tau;}}_2+\frac{1}{2}A{\mathrm{\&tau;}}_1^2,l_1=l_s+v_s{T}_1+\frac{1}{2}{a}_s{T}_1^2+\frac{1}{6}J{T}_1^3{,}^{}{t}_1\&le;t\&le;t_2\\ l_2+f_2{\mathrm{\&tau;}}_3+\frac{1}{2}A{\mathrm{\&tau;}}_3^2-\frac{1}{6}J{\mathrm{\&tau;}}_3^3,l_2=l_1+f_1{T}_2+\frac{1}{2}A{T}_1^2,t_2\&le;t\&le;t_3\\ l_3+f_3{\mathrm{\&tau;}}_4,l_3=l_2+f_2{T}_3+\frac{1}{2}A{T}_3^2-\frac{1}{6}J{T}_3^3,t_3\&le;t\&le;t_4\\ l_4+f_4{\mathrm{\&tau;}}_5-\frac{1}{6}J{\mathrm{\&tau;}}_5^3,f=l_3+f_3{T}_4,t_4\&le;t\&le;t_5\\ l_5+f_5{\mathrm{\&tau;}}_6-\frac{1}{62}D{\mathrm{\&tau;}}_6^2,f_5=l_4+f_4{T}_5-\frac{1}{6}J{T}_5^3,t_5\&le;t\&le;t_6\\ l_6+f_6{\mathrm{\&tau;}}_7-\frac{1}{2}D{\mathrm{\&tau;}}_7^2+\frac{1}{6}J{\mathrm{\&tau;}}_7^2,f_6=l_5+f_5{T}_6-\frac{1}{2}D{T}_6^2,t_6\&le;t\&le;t_7\end{array}\right.$

Wherein, t is time coordinate, t _i(i=1,2,3 ..., 7) and be the time coordinate at each stage end, τ _iExpression local time is to deduct τ with time t in each stage _iThe time value that obtains, T _i(i=1,2,3 ..., 7) and represent the time span that each stage continues, A is peak acceleration, and D is maximum deceleration, and J is maximum acceleration;

The speed planning processing unit, the described acceleration system of equations (5), described rate equation group (6) and the described shifted systems (7) that are used for obtaining according to described stage system of equations acquiring unit carry out the planning of S type curve speed to described i+1 section machining locus.

11. acceleration/deceleration control device according to claim 10 is characterized in that, described speed planning processing unit comprises:

Interval differentiation subelement is used for calculating the time span that each stage continues, and obtains according to described acceleration system of equations (5):

$T_1=\frac{A-a_s}{J},$ $T_3=\frac{A}{J},$ $T_5=\frac{D}{J},$ $T_7=\frac{D-a_e}{J},$

Wherein, T ₁The time span that continues for adding boost phase, T ₃The time span that continues for subtracting boost phase, T ₅Be lasting time span of acceleration and deceleration stage, T ₇For subtracting the time span that the decelerating phase continues;

Reach speed f at even boost phase end ₃, according to described rate equation group (6) and described shifted systems (7), obtain:

f ₃=f （8）；

$T_2=\frac{f-v_s}{A}-\frac{A}{J}+\frac{a_s^2}{2\mathrm{AJ}}---\left(9\right);$

Wherein, f is speed of feed, T ₂For the lasting time span of even boost phase, if T ₂﹤ 0, passes through formula $A=\mathrm{sgn}\left(A\right)\sqrt{J-(f-v_s)+\frac{a_s^2}{2}}---\left(10\right)$

The value of adjusting peak acceleration A is the maximum possible value, and substitution formula (9) recomputates T ₂Value;

Reach speed v subtracting decelerating phase end _e, according to described rate equation group (6) and described shifted systems (7), obtain:

$T_6=\frac{f-v_e}{D}-\frac{D}{J}+\frac{a_e^2}{2\mathrm{DJ}}---\left(11\right)$

Wherein, T ₆For lasting time span of even decelerating phase, if T ₆﹤ 0, passes through formula

$D=\mathrm{sgn}\left(D\right)\sqrt{J(f-v_e)+\frac{a_e^2}{2}}---\left(12\right)$

The value of adjusting maximum deceleration D is the maximum possible value, and substitution formula (11) is counted T again ₆Value

With T ₁, T ₂, T ₃, T ₅, T ₆, T ₇Value substitution rate equation group (6), in conjunction with $L=\underset{k=1}{\overset{7}{\mathrm{\&Sigma;}}}{l}_k-l_{k-1}=l_7-l_s,$ Can get:

$T_4=\frac{1}{f}(\frac{v_e{a}_e+v_s{a}_s}{J}-\frac{a_e^3+a_s^3}{3J^2})-$

$\frac{1}{f}[\frac{1}{2A+2D}{f}^2+(\frac{A}{2J}+\frac{D}{2J})f+\frac{A(v_s-\frac{a_s^2}{2J})}{2J}+\frac{D(v_e-\frac{a_e^2}{2J})}{2J}-\frac{{(v_s-\frac{a_s^2}{2J})}^2}{2A}-\frac{(v_e-\frac{a_e^2}{2J})}{2D}]$

Wherein, T ₄Be the length of duration in stage at the uniform velocity, L is the length of i+1 section machining locus, l ₇For subtracting displacement corresponding to decelerating phase, l _sBe initial position, if T ₄﹤ 0, and the value of adjusting speed of feed f makes T ₄=0, and recomputate T ₁, T ₂, T ₃, T ₅, T ₆And T ₇Value;

The real-time interpolation subelement is used for according to the described interval T that subelement obtains that differentiates ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇Value S type curve carried out real-time interpolation calculate.

12. a numerically-controlled machine is characterized in that, described numerically-controlled machine comprises according to claim 7-11 described acceleration/deceleration control devices of any one.

Images